Until Wednesday, Gov. Jan Brewer, R-Ariz., had kept the door open to running for another term. But with the announcement that she won't seek reelection in 2014, Brewer can consider a different political future.

Though her national profile may not draw a lot of crossover appeal from Democrats and independents, there's a wide open Republican presidential primary coming in 2016, and governors (incumbent and former) have often used their posts as a possible springboard to higher office. A recent forum on conservative commentator Sean Hannity's website spent six pages debating the question: Could Jan Brewer run for president?

Not so fast, say several Republican strategists. A Brewer bid is not only unlikely, but inadvisable, too.

"If she jumps in the race for president, she would be adding to the current pool of polarizing and unelectable candidates who are a distraction to the viable," said Trey Hardin, a strategist who has worked on the campaigns of several Republican candidates.

Rick Wilson, a Florida-based GOP consultant, said a run for president is "out of the range of possibility," and John Feehery, another Republican strategist said he "can't imagine she could do much after her tenure as governor."

But Chuck Coughlin, a longtime adviser to Brewer, said the governor's record as a pragmatic problem-solver in Arizona runs far deeper than the handful of topics that have made national news. He pointed to her success in passing five Republican budgets in a row, securing voter approval for a sales tax hike in 2010 that helped cover education funding, and expanded Medicaid under the Affordable Care Act over conservative opposition.

He doesn't think a presidential bid is in the cards - though "I'm sure she'd be flattered to be considered," he said - but that she would prefer to work on public health issues, a longtime passion, resolving the immigration debate, or helping Phoenix win a bid to host the 2016 Republican convention.

Rather than interest in the job, a bigger problem could be electability. Although Brewer could fire up the conservative base, she would "not be a big draw for the Hispanic vote," said strategist Ron Bonjean.

"Nationally she came across as a very controversial figure. It's among Republican primary voters she is popular. But among independents, among much of the rest of the country, she has turned them off," he said.

Still, Coughlin said he was confident that a Senate bid "wouldn't be in the cards" because of Brewer's longtime friendship with McCain.

"Despite the disagreements, she's been a lifelong supporter of his and he has been very good with her," he said, noting that McCain would often introduce her when she was campaigning in the 2010 gubernatorial race.

She wants to see the GOP regain the White House, he said, and would be happy to support the people who share that ambition.